Your choices:
Test chosen: Sample size for unpaired t test
Expected SD of each group = 65
Significance level (alpha) = 0.05 (two-tailed)
Detailed explanation:
You requested a detailed explanation for N = 25 and power = 80%.
Assume that the true difference between means is 52.68. Now imagine that you perform
many experiments, with N = 25 per group in each experiment. Due to random sampling,
you won't find that the difference between means equals 52.68 in every experiment.
Instead, you'll find that the difference between means will be greater than 52.68 in about
half the experiments, and less than 52.68 in the other half.
In 80% (the power) of those experiments, the P value will be less than 0.05 (two-tailed)
so the results will be deemed "statistically significant". In the remaining 20% of the
experiments, the difference between means will be deemed "not statistically significant",
so you will have made a Type II (beta) error.
Summary: A sample size of 25 in each group has a 80% power to detect a difference
between means of 52.68 with a significance level (alpha) of 0.05 (two-tailed).
Alternative explanation using confidence intervals:
If you perform many experiments with N = 25 in each group, you expect that in 80% of
these experiments (the power), the width of the 95% confidence interval for the
difference between means will extend 52.68 or less in each direction. In the remaining
20% of the experiments, you will expect the 95% confidence interval to be wider than
that.
Table of tradeoffs:
For any combination of sample size (N) and power, this table shows the difference
between means that can be detected.
Power
N per group
99%
95%
90%
80%
50%
3
289.41
243.40
218.87
189.17
132.34
4
232.76
195.76
176.03
152.14
106.43
5
200.19
168.36
151.40
130.85
91.54
6
178.37
150.01
134.89
116.59
81.56
7
162.44
136.61
122.84
106.17
74.28
8
150.14
126.27
113.54
98.13
68.65
9
140.28
117.97
106.08
91.69
64.14
10
132.14
111.13
99.93
86.37
60.42
12
119.37
100.39
90.28
78.02
54.58
14
109.72
92.27
82.97
71.71
50.17
16
102.08
85.85
77.20
66.72
46.68
18
95.84
80.61
72.48
62.65
43.83
20
90.63
76.22
68.54
59.24
41.44
25
80.59
67.78
60.95
52.68
36.85
30
73.29
61.64
55.42
47.90
33.51
35
67.67
56.91
51.17
44.23
30.94
40
63.17
53.13
47.77
41.29
28.88
50
56.34
47.38
42.61
36.83
25.76
60
51.34
43.17
38.82
33.55
23.47
70
47.47
39.92
35.90
31.02
21.70
80
44.36
37.30
33.54
28.99
20.28
90
41.79
35.14
31.60
27.31
19.11
100
39.62
33.32
29.96
25.89
18.12
150
32.29
27.16
24.42
21.10
14.76
200
27.94
23.50
21.13
18.26
12.77
300
22.79
19.17
17.23
14.90
10.42
400
19.73
16.59
14.92
12.89
9.02
500
17.64
14.84
13.34
11.53
8.07
1000
12.47
10.48
9.43
8.15
5.70
If you want to use unequal N:
Instead of using 25 subjects in each group, you can use unequal N. Substitute any of the
following experimental designs, without losing any statistical power. Note that total
sample size increases if you use unequal N (you must increase N for Group B more than
you decrease N for group A). This can make sense if treatment A "costs" more
(considering expense, hassle and risk) than treatment B. Even though the total sample
size goes up, choosing unequal N may reduce the total cost (or risk) of the experiment.
Sample size
Group A
Group B
Ratio
Total
25
25
1.000
50
23
29
1.250
52
21
32
1.500
53
19
38
2.000
57
17
51
3.000
68
16
64
4.000
80
15
75
5.000
90
When to choose
If the "cost" of treatment A is 1.0 times
the "cost" of treatment B.
If the "cost" of treatment A is 1.6 times
the "cost" of treatment B.
If the "cost" of treatment A is 2.3 times
the "cost" of treatment B.
If the "cost" of treatment A is 4.0 times
the "cost" of treatment B.
If the "cost" of treatment A is 9.0 times
the "cost" of treatment B.
If the "cost" of treatment A is 16.0 times
the "cost" of treatment B.
If the "cost" of treatment A is 25.0 times
the "cost" of treatment B.
You cannot reduce the sample size of Group A to fewer than half the number needed if
you choose equal sample size (without losing statistical power).
Report created by GraphPad StatMate 2.00. 3/1/2004 10:31:26 AM